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The hyperKähler geometry associated to Wolf spaces

Piotr Kobak, Andrew Swann (2001)

Bollettino dell'Unione Matematica Italiana

Sia G un grupo di Lie compatto e semplice. Sia O min la più piccola orbita nilpotente non-banale nell'algebra di Lie complessa g C . Si presenta una costruzione diretta di teoria di Lie delle metriche iperKahler su O min con potenziale Kahleriano G -invariante e compatibili con la forma simplettica complessa di Kostant-Kirillov-Souriau. In particolare si ottengono le metriche iperKahler dei fibrati associati sugli spazi di Wolf (spazi simmetrici quaternionali a curvatura scalare positiva).

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